The concept of pain had never factored into the sensory sphere of the liquid machine. Pain was an indicator of damage to a part of the organism, but this organism didn't have parts, except on a purely molecular level and its molecules were each primitive, miniaturized versions of the total machine. If any section were parted, the separated parts would revert to liquid metal poly-alloy. The only default command implemented on the molecular level of this design was to find the main mass again and rejoin it as soon as possible. Each molecule had a range of fourteen kilometers..

As it is mentioned above, it was not one machine, but several nano machines working together. When he falls into molten steel, the heat melt its nano parts thus causing disruptions in its system.

From same page,

Keep in mind this is not one machine, its thousands of nano machines working together. The heat was melting the structure causing disruptions in the system, making T-1000 move in every possible way. The T-1000 didn't know what to do, that's why he kept bringing up all the data he had, showing all the copied characters. According to James Cameron in T2 Extreme DVD audio commentary, it was looking for solution.

In the novelization, it was stated that all its molecules were searching for the right channels back into its proper structure, but the extreme heat and great amount of the molten metal around it confused them. That's why he couldn't get his shape back and died.

From the same link,

Novelization: It was screaming. A terrifying, inhuman siren of scream, as all its molecules were searching for the right channels back into its proper structure, but the intense heat and volubility of the molten metal around it confused them.

Adding to TL;DR’s response, there’s one piece in the movie which might give away that something’s wrong with the T-1000.

After it reassembles from the liquid nitrogen spill, it starts walking towards John, Sarah, and the Terminator. As it’s doing so, it has to get around a waist high metal structure. It tried walking right through, but as its hand makes contact with the metal structure, it gets stuck. To me, that tells me the nitrogen spill did some permanent damage to it.

Not sure if that part is in the original or just an uncut version. Hope that helped you even more.